Quadratic maps and smooth vector-valued functions: Euler characteristics of level sets
- 56 Downloads
Quadratic maps of RN into RK are studied. Explicit expressions are obtained for the Euler characteristics of level sets of such maps. The Euler characteristics of level sets of smooth vector-valued functions are also evaluated in terms of their values at critical points.
KeywordsExplicit Expression Euler Characteristic
Unable to display preview. Download preview PDF.
- 1.A. A. Agrachev and R. V. Gamkrelidze, “Calculation of the Euler characteristic of intersections of real quadrics,” Dokl. Akad. Nauk SSSR,299, No. 1, 11–14 (1988).Google Scholar
- 2.R. Rockafellar, Convex Analysis, Princeton University Press, Princeton, N.J. (1970).Google Scholar
- 3.R. Thom and H. I. Levine. “Singularities of differentiable maps,” in: Singularities of Differentiable Maps [in Russian], Mir, Moscow (1968), pp. 9–101.Google Scholar
- 4.A. N. Tyurin, “On intersection of quadrics,” Usp. Mat. Nauk,30, No. 6, 51–100 (1975).Google Scholar
- 5.M. W. Hirsch, Differential Topology, Springer, New York (1976).Google Scholar
- 6.R. Abraham and J. Robbin, Transversal Mappings and Flows, Benjamin, New York (1967).Google Scholar
- 7.I. G. Petrowsky, “On the topology of real plane algebraic curves,” Ann. Math.,39, 189–396 (1938).Google Scholar